The Dual Air was a tilt valve second stage, so you have either a Hydro Twin(unbalanced) or a hydro Twin II(balanced). I suspect that since you have orange under the Scuba pro sticker that you have a Hydro twin II, since the Hydro Twin had a blue and silver sticker:
The Scuba Museum website has some very good photos of these regs and I would suggest you check out his site. The Hydro Twin II has a shorter balance chamber where the hp diaphragm is located and has an 8 sided nut. If the back of your reg looks like this, it's a Hydro Twin II -
http://thescubamuseum.com/regulatorsusa ... 20PICS.htm
The Hydro Twin has a 'taller' chamber with a 2 sided chunk of metal that the allen nut sits in.
I find it interesting that you have a Sportsways reg, with a HW mouthpiece and a Scuba Pro sticker... Given the SW, LeCocq, HW and Scubapro histories, I can't help but wonder if this was someone's attempt at ironic humor or something.
Great gift by the way.
EDIT: So I think you have a Hydro Twin II: I just realized there is no nut at the end of the long cylinder piece on the right side of the first stage( cannot for the life of me remember what it was for ). The balanced version did not have the nut, the unbalanced regs did..... like this one....

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